1. Field of the Invention
The present invention relates to electronic network analysis, and more particularly, to methods and apparatus for processing data samples indicating the transmission or reflection characteristics of an electronic network.
2. Description of Related Art
Network analyzers, such as the WILTRON 360, available through WILTRON, 490 Jarvis Drive, Morgan Hill, Calif. 95037, measure the real and imaginary components of the reflection and transmission coefficients of a network over a range of equally-spaced frequencies between operator-delivered frequencies f1 and f2. The analyzer will display the results of the measurements in a real and imaginary format, or they can be converted to magnitude and phase and displayed in a variety of graph types for the user's convenience. One technique, which has proven useful in practice, for analyzing the measurements, involves taking the data measured in a frequency domain and converting it to the time domain by means of an inverse Fourier transform. The Fourier transform will give the response of the network in the time domain. With time domain data, the results of the measurements can be used to determine distances in the network to discontinuities reflected in the data, because time is directly related to distance through the network by the velocity of propagation of the signals through the network. Therefore, this technique is useful for analyzing complex electronic networks in order to isolate discontinuities.
If only the magnitudes and locations of various discontinuities are to be determined, it is then a simple matter to transform the frequency domain data exactly as it is measured. However, it is possible to increase the utility of the time domain data by performing additional processing steps to identify correct phase measurements for the data.
In the prior art, a true low-pass algorithm has been utilized to construct the additional time domain data reflecting accurate phase information. However, for the true low-pass algorithm, f1 must be zero. The algorithm works by constructing a complete double-sided spectrum from -f2 to f2 by taking the complex conjugate of the data at each positive frequency and placing it at the corresponding negative frequency as shown below.
______________________________________ DATA FROM MEASUREMENT 0 f2 FREQUENCY DOMAIN x1 x2 x3 . . . xn (real part of data) 0 y2 y3 . . . yn (imaginary part) CONSTRUCTED COMPLEX CONJUGATE SPECTRUM -f2 0 f2 FREQUENCY DOMAIN xn . . . x3 x2 x1 x2 x3 . . . xn (real part) -yn . . . -y3 -y2 0 y2 y3 . . . yn (imaginary part) ______________________________________
The inverse Fourier transform of the constructed complex conjugate spectrum is real, that is, the imaginary part is zero for all data samples as shown below.
______________________________________ 0 t TIME DOMAIN x1 x2 x3 . . . (real part) 0 0 0 . . . (imaginary part) ______________________________________
From the real part of the transform, it is possible to deduce not only the magnitude of the network discontinuities, but their nature. If the discontinuity consists of a change in impedance, that fact can be recognized and an increase of impedance can be distinguished from a decrease. If a discontinuity is reactive, it can be identified as inductive or capacitive. The location of each discontinuity can be determined within the resolution limits of the measurement.
This true low pass method has been used for a number of years. However, it is subject to the constraint that the measured data must be available with the entire spectrum down to zero frequency (f1 must be zero). If the reflection of interest is from a narrow band circuit, such as a filter or wave guide, the true low pass method cannot be used. Further, for equipment that is incapable of providing equal frequency steps all the way down to zero frequency, the true low pass method is unavailable.
Thus, in the more general case, f1 is not zero. The missing information from the unmeasured part of the spectrum between zero frequency and fl, causes a distortion in the time domain response.
Another source of distortion is the phase rotation in the time domain which is an unavoidable consequence of transforming a single sided spectrum. The arbitrary phase rotation which appears in this case makes it impossible, using prior art techniques, to determine the nature of the discontinuity at a given distance.
Accordingly, there is a need for apparatus and methods for processing data measured over a range of frequencies from f1 to f2 where f1 is greater than zero. In particular, it is desirable to identify accurate phase information for data samples of interest in the time domain where the complete complex conjugate spectrum is unavailable.